Hierarchical music structure analysis, modeling and resynthesis : a dynamical systems and signal processing approach

Abstract

The problem of creating generative music systems has been approached in different ways, each guided by different goals, aesthetics, beliefs and biases. These generative systems can be divided into two categories: the first is an ad hoc definition of the generative algorithms, the second is based on the idea of modeling and generalizing from preexistent music for the subsequent generation of new pieces. Most inductive models developed in the past have been probabilistic, while the majority of the deductive approaches have been rule based, some of them with very strong assumptions about music. In addition, almost all models have been discrete, most probably influenced by the discontinuous nature of traditional music notation. We approach the problem of inductive modeling of high level musical structures from a dynamical systems and signal processing perspective, focusing on motion per se independently of particular musical systems or styles. The point of departure is the construction of a state space that represents geometrically the motion characteristics of music. We address ways in which this state space can be modeled deterministically, as well as ways in which it can be transformed to generate new musical structures. Thus, in contrast to previous approaches to inductive music structure modeling, our models are continuous and mainly deterministic.

(cont.) We also address the problem of extracting a hierarchical representation of music from the state space and how a hierarchical decomposition can become a second source of generalization.